These worked for me when I started waking up with anxiety attacks a few years ago, maybe they'll work for you.
  1. Pick something you love and do the ABC's with it.
    Sci-Fi authors, grunge band song titles, characters from Shakespearian plays, whatever works. For me it's authors: A for Atwood, B for Byatt, etc.
  2. Have a dram of whisky.
    Not more than one glass, otherwise it has the opposite effect. (Does this break the non-pharmaceutical rule? I vote no.)
  3. Replay your favorite TV episodes in your head with yourself as an additional main character.
    For me it's Firefly. Kaylee and I are BFFs in my version.
  4. Have sex
    I don't know how to put this delicately... Orgasms make you sleepy. If you don't have an S.O. who's game, there are single-player alternatives.
  5. Get up and read.
    If it's just not happening, at least do something to get you out of the endless loop of anxiety in your head. TV is a stimulant, but reading may calm your restless thoughts, and for many people it does make them sleepy.
  6. Go outside
    This is obviously not an immediate solution, I don't recommend walking the streets in the middle of the night; but if the above don't work, go outside the next day and wear yourself out with physical activity.
  7. Go see a doctor.
    If it goes on too long, please go see a doctor. Stress is very bad for you, lack of sleep is worse. They can lead to depression and all sorts of scary things. Be kind to yourself and get some help.